Question

8square root 3(3 - 10square root 7)

Answer 1

To simplify the expression \( 8\sqrt{3}(3 - 10\sqrt{7}) \), we can distribute \( 8\sqrt{3} \) across the terms inside the parentheses.

1. Distributing \( 8\sqrt{3} \):
\[
8\sqrt{3} \cdot 3 - 8\sqrt{3} \cdot 10\sqrt{7}
\]

2. Now, calculating each part:
- For the first term:
\[
8\sqrt{3} \cdot 3 = 24\sqrt{3}
\]

- For the second term:
\[
8\sqrt{3} \cdot 10\sqrt{7} = 80\sqrt{21}
\]
(since \( \sqrt{3} \cdot \sqrt{7} = \sqrt{21} \))

3. Combining these results:
\[
24\sqrt{3} - 80\sqrt{21}
\]

Thus, the simplified expression is:
\[
\boxed{24\sqrt{3} - 80\sqrt{21}}
\]